Tianyu Jin

Tianyu Jin, Georg Maierhofer, Katharina Schratz et al.

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of larger time steps, and better structure preservation properties. However, this comes at the price of having to solve a nonlinear equation at every time step of the numerical scheme. In this work, we propose a novel deep learning based hybrid Newton's method to accelerate this solution of the nonlinear time step system for stiff time-evolution nonlinear equations. We propose a targeted learning strategy which facilitates robust unsupervised learning in an offline phase and provides a highly efficient initialisation for the Newton iteration leading to consistent acceleration of Newton's method. A quantifiable rate of improvement in Newton's method achieved by improved initialisation is provided and we analyse the upper bound of the generalisation error of our unsupervised learning strategy. These theoretical results are supported by extensive numerical results, demonstrating the efficiency of our proposed neural hybrid solver both in one- and two-dimensional cases.

Yue Wu, Tianyu Jin, Chuqi Chen et al.

We propose an energy stable network (EStable-Net) for solving gradient flow equations. The EStable-Net enables decreasing of a discrete energy along the neural network, which is consistent with the property of the gradient flow equation. The architecture of the neural network EStable-Net is based on the block network structure (Autoflow) in which output of each block can be interpreted as an intermediate state of the evolution process of the equation, and the energy stable property is incorporated in each block, which is easily generalized to include other physical and/or numerical properties. Our EStable-Net is a supervised learning network approach for solving evolution equations which does not depend on the convergence of time step goes to 0, and can be applied generally even when only data is available but the equation is unknown. We also propose a training strategy for supervised learning that employs data of the evolution stages with different nature. The EStable-Net is validated by numerical experimental results based on the Allen-Cahn equation and the Cahn-Hilliard equation in two dimensions.

Tianyu Jin, Shuo Chen, Yida Wang et al.

Long-horizon strategic planning in complex strategy games demands concurrent reasoning across multiple decision domains under imperfect information and sparse reward. Existing LLM-based agents suffer from three systematic failures: scene blindness from raw tile coordinates, context overflow and domain coupling from monolithic state dumps, and shallow cross-game learning that treats each episode in isolation. We present SAGA, an LLM multi-agent framework with three mechanisms each directly targeting one class of failure: (i) a Map-Semantic Scene Graph that encodes typed spatial relations among game entities into per-unit natural-language context, resolving spatial blindness without global token inflation; (ii) a Tool-Augmented Planner that pulls fine-grained domain state on demand and dispatches per-domain directives to dedicated specialist controllers, eliminating context overflow, domain coupling, and mechanical constraint violations; and (iii) a Dual-Horizon Feedback Loop that combines periodic within-game goal generation with structured cross-game causal post-mortem, enabling principled strategic evolution without manual reward engineering. Evaluated on FreeCiv, SAGA attains the highest mean civilization score -- the environment's sole sparse objective reward -- with lower variance than the two strongest baselines, and is the only method that significantly surpasses every baseline on infrastructure construction, the resource axis most readily sacrificed under multi-objective conflict. It outscores the two strongest baselines in most head-to-head games while cutting output tokens (the dominant decoding cost) by 27%. Equipped with the cross-game evolution module, SAGA reaches the highest end-of-chain score across five successive episodes. Ablation studies confirm that each architectural component contributes independently to this advantage.